If $\left|\begin{array}{ccc}{}^9\mathrm{C}_4& {}^9\mathrm{C}_5& {}^{10}\mathrm{C}_{\mathrm{r}}\\ {}^{10}\mathrm{C}_6& {}^{10}\mathrm{C}_7& {}^{11}\mathrm{C}_{\mathrm{r}+2}\\ {}^{11}\mathrm{C}_8& {}^{11}\mathrm{C}_9& {}^{12}\mathrm{C}_{\mathrm{r}+4}\end{array}\right| = 0$ then the value of r is equal to

Given $\left|\begin{array}{ccc}{}^9\mathrm{C}_4& {}^9\mathrm{C}_5& {}^{10}\mathrm{C}_{\mathrm{r}}\\ {}^{10}\mathrm{C}_6& {}^{10}\mathrm{C}_7& {}^{11}\mathrm{C}_{\mathrm{r}+2}\\ {}^{11}\mathrm{C}_8& {}^{11}\mathrm{C}_9& {}^{12}\mathrm{C}_{\mathrm{r}+4}\end{array}\right| = 0$

$$\begin{gathered} {\mathrm{C}}_2\to {\mathrm{C}}_1+{\mathrm{C}}_2 \\ \left|\begin{array}{ccc}{}^9\mathrm{C}_4& {}^{10}\mathrm{C}_5& {}^{10}\mathrm{C}_{\mathrm{r}}\\ {}^{10}\mathrm{C}_6& {}^{11}\mathrm{C}_7& {}^{11}\mathrm{C}_{\mathrm{r}+2}\\ {}^{11}\mathrm{C}_8& {}^{12}\mathrm{C}_9& {}^{12}\mathrm{C}_{\mathrm{r}+4}\end{array}\right| = 0 \end{gathered}$$

for $\mathrm{r}=5, {\mathrm{C}}_2$ is same as ${\mathrm{C}}_3$